First, 綺麗な字 doesn’t show up in the translation at all. Second, I think this translation is misleading if the expected answer is ような. Since the translation says the person writes (a verb) like they are using a 筆, I would expect the answer to be ように. With ような, the translation would have to be something more like “That person writes pretty characters that are written as if by a fude” (or a less awkward version of that).
Are there any issues with my logic here?
P.S. まるで also doesn’t show up in the translation, and there’s also nothing in the translation indicating why 書けます instead of 書きます is used.